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<div class="header">
  <div class="summary">
<a href="classEigen_1_1SVDBase-members.html">List of all members</a> &#124;
<a href="#pub-types">Public Types</a> &#124;
<a href="#pub-methods">Public Member Functions</a> &#124;
<a href="#pro-methods">Protected Member Functions</a>  </div>
  <div class="headertitle">
<div class="title">Eigen::SVDBase&lt; Derived &gt; Class Template Reference<div class="ingroups"><a class="el" href="group__DenseLinearSolvers__chapter.html">Dense linear problems and decompositions</a> &raquo; <a class="el" href="group__DenseLinearSolvers__Reference.html">Reference</a> &raquo; <a class="el" href="group__SVD__Module.html">SVD module</a></div></div>  </div>
</div><!--header-->
<div class="contents">
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><h3>template&lt;typename Derived&gt;<br />
class Eigen::SVDBase&lt; Derived &gt;</h3>

<p>Base class of SVD algorithms. </p>
<dl class="tparams"><dt>Template Parameters</dt><dd>
  <table class="tparams">
    <tr><td class="paramname">Derived</td><td>the type of the actual SVD decomposition</td></tr>
  </table>
  </dd>
</dl>
<p>SVD decomposition consists in decomposing any n-by-p matrix <em>A</em> as a product </p><p class="formulaDsp">
\[ A = U S V^* \]
</p>
<p> where <em>U</em> is a n-by-n unitary, <em>V</em> is a p-by-p unitary, and <em>S</em> is a n-by-p real positive matrix which is zero outside of its main diagonal; the diagonal entries of S are known as the <em>singular</em> <em>values</em> of <em>A</em> and the columns of <em>U</em> and <em>V</em> are known as the left and right <em>singular</em> <em>vectors</em> of <em>A</em> respectively.</p>
<p>Singular values are always sorted in decreasing order.</p>
<p>You can ask for only <em>thin</em> <em>U</em> or <em>V</em> to be computed, meaning the following. In case of a rectangular n-by-p matrix, letting <em>m</em> be the smaller value among <em>n</em> and <em>p</em>, there are only <em>m</em> singular vectors; the remaining columns of <em>U</em> and <em>V</em> do not correspond to actual singular vectors. Asking for <em>thin</em> <em>U</em> or <em>V</em> means asking for only their <em>m</em> first columns to be formed. So <em>U</em> is then a n-by-m matrix, and <em>V</em> is then a p-by-m matrix. Notice that thin <em>U</em> and <em>V</em> are all you need for (least squares) solving.</p>
<p>The status of the computation can be retrieved using the <em><a class="el" href="classEigen_1_1SVDBase.html#a06c311bc452dc1ca5abce2f640e15292" title="Reports whether previous computation was successful.">info()</a></em> method. Unless <em><a class="el" href="classEigen_1_1SVDBase.html#a06c311bc452dc1ca5abce2f640e15292" title="Reports whether previous computation was successful.">info()</a></em> returns <em>Success</em>, the results should be not considered well defined.</p>
<p>If the input matrix has inf or nan coefficients, the result of the computation is undefined, and <em><a class="el" href="classEigen_1_1SVDBase.html#a06c311bc452dc1ca5abce2f640e15292" title="Reports whether previous computation was successful.">info()</a></em> will return <em>InvalidInput</em>, but the computation is guaranteed to terminate in finite (and reasonable) time. </p><dl class="section see"><dt>See also</dt><dd>class <a class="el" href="classEigen_1_1BDCSVD.html" title="class Bidiagonal Divide and Conquer SVD">BDCSVD</a>, class <a class="el" href="classEigen_1_1JacobiSVD.html" title="Two-sided Jacobi SVD decomposition of a rectangular matrix.">JacobiSVD</a> </dd></dl>
</div><div id="dynsection-0" onclick="return toggleVisibility(this)" class="dynheader closed" style="cursor:pointer;">
  <img id="dynsection-0-trigger" src="closed.png" alt="+"/> Inheritance diagram for Eigen::SVDBase&lt; Derived &gt;:</div>
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<div id="dynsection-0-content" class="dyncontent" style="display:none;">
<div class="center"><img src="classEigen_1_1SVDBase__inherit__graph.png" border="0" usemap="#aEigen_1_1SVDBase_3_01Derived_01_4_inherit__map" alt="Inheritance graph"/></div>
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<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-types"></a>
Public Types</h2></td></tr>
<tr class="memitem:a6229a37997eca1072b52cca5ee7a2bec"><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SVDBase.html#a6229a37997eca1072b52cca5ee7a2bec">Index</a></td></tr>
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<tr class="inherit_header pub_types_structEigen_1_1EigenBase"><td colspan="2" onclick="javascript:toggleInherit('pub_types_structEigen_1_1EigenBase')"><img src="closed.png" alt="-"/>&#160;Public Types inherited from <a class="el" href="structEigen_1_1EigenBase.html">Eigen::EigenBase&lt; Derived &gt;</a></td></tr>
<tr class="memitem:a554f30542cc2316add4b1ea0a492ff02 inherit pub_types_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">typedef <a class="el" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a></td></tr>
<tr class="memdesc:a554f30542cc2316add4b1ea0a492ff02 inherit pub_types_structEigen_1_1EigenBase"><td class="mdescLeft">&#160;</td><td class="mdescRight">The interface type of indices.  <a href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">More...</a><br /></td></tr>
<tr class="separator:a554f30542cc2316add4b1ea0a492ff02 inherit pub_types_structEigen_1_1EigenBase"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:a705a7c2709e1624ccc19aa748a78d473"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SVDBase.html#a705a7c2709e1624ccc19aa748a78d473">computeU</a> () const</td></tr>
<tr class="separator:a705a7c2709e1624ccc19aa748a78d473"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a5f12efcb791eb007d4a4890ac5255ac4"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SVDBase.html#a5f12efcb791eb007d4a4890ac5255ac4">computeV</a> () const</td></tr>
<tr class="separator:a5f12efcb791eb007d4a4890ac5255ac4"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a06c311bc452dc1ca5abce2f640e15292"><td class="memItemLeft" align="right" valign="top"><a class="el" href="group__enums.html#ga85fad7b87587764e5cf6b513a9e0ee5e">ComputationInfo</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SVDBase.html#a06c311bc452dc1ca5abce2f640e15292">info</a> () const</td></tr>
<tr class="memdesc:a06c311bc452dc1ca5abce2f640e15292"><td class="mdescLeft">&#160;</td><td class="mdescRight">Reports whether previous computation was successful.  <a href="classEigen_1_1SVDBase.html#a06c311bc452dc1ca5abce2f640e15292">More...</a><br /></td></tr>
<tr class="separator:a06c311bc452dc1ca5abce2f640e15292"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:afc7fe1546b0f6e1801b86f22f5664cb8"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1Matrix.html">MatrixUType</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SVDBase.html#afc7fe1546b0f6e1801b86f22f5664cb8">matrixU</a> () const</td></tr>
<tr class="separator:afc7fe1546b0f6e1801b86f22f5664cb8"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a245a453b5e7347f737295c23133238c4"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1Matrix.html">MatrixVType</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SVDBase.html#a245a453b5e7347f737295c23133238c4">matrixV</a> () const</td></tr>
<tr class="separator:a245a453b5e7347f737295c23133238c4"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:afe8a555f38393a319a71ec0f0331c9ef"><td class="memItemLeft" align="right" valign="top"><a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SVDBase.html#afe8a555f38393a319a71ec0f0331c9ef">nonzeroSingularValues</a> () const</td></tr>
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<tr class="memitem:a30b89e24f42f1692079eea31b361d26a"><td class="memItemLeft" align="right" valign="top"><a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SVDBase.html#a30b89e24f42f1692079eea31b361d26a">rank</a> () const</td></tr>
<tr class="separator:a30b89e24f42f1692079eea31b361d26a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a1c95d05398fc15e410a28560ef70a5a6"><td class="memItemLeft" align="right" valign="top">Derived &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SVDBase.html#a1c95d05398fc15e410a28560ef70a5a6">setThreshold</a> (const RealScalar &amp;<a class="el" href="classEigen_1_1SVDBase.html#a98b2ee98690358951807353812a05c69">threshold</a>)</td></tr>
<tr class="separator:a1c95d05398fc15e410a28560ef70a5a6"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a27586b69dbfb63f714d1d45fd6304f97"><td class="memItemLeft" align="right" valign="top">Derived &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SVDBase.html#a27586b69dbfb63f714d1d45fd6304f97">setThreshold</a> (Default_t)</td></tr>
<tr class="separator:a27586b69dbfb63f714d1d45fd6304f97"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a4e7bac123570c348f7ed6be909e1e474"><td class="memItemLeft" align="right" valign="top">const SingularValuesType &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SVDBase.html#a4e7bac123570c348f7ed6be909e1e474">singularValues</a> () const</td></tr>
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<tr class="memitem:ab28499936c0764fe5b56b9f4de701e26"><td class="memTemplParams" colspan="2">template&lt;typename Rhs &gt; </td></tr>
<tr class="memitem:ab28499936c0764fe5b56b9f4de701e26"><td class="memTemplItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1Solve.html">Solve</a>&lt; Derived, Rhs &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classEigen_1_1SVDBase.html#ab28499936c0764fe5b56b9f4de701e26">solve</a> (const <a class="el" href="classEigen_1_1MatrixBase.html">MatrixBase</a>&lt; Rhs &gt; &amp;b) const</td></tr>
<tr class="separator:ab28499936c0764fe5b56b9f4de701e26"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a98b2ee98690358951807353812a05c69"><td class="memItemLeft" align="right" valign="top">RealScalar&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SVDBase.html#a98b2ee98690358951807353812a05c69">threshold</a> () const</td></tr>
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<tr class="inherit_header pub_methods_classEigen_1_1SolverBase"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_classEigen_1_1SolverBase')"><img src="closed.png" alt="-"/>&#160;Public Member Functions inherited from <a class="el" href="classEigen_1_1SolverBase.html">Eigen::SolverBase&lt; SVDBase&lt; Derived &gt; &gt;</a></td></tr>
<tr class="memitem:ae1025416bdb5a768f7213c67feb4dc33 inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">const AdjointReturnType&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#ae1025416bdb5a768f7213c67feb4dc33">adjoint</a> () const</td></tr>
<tr class="separator:ae1025416bdb5a768f7213c67feb4dc33 inherit pub_methods_classEigen_1_1SolverBase"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a1fbabe7f12bcbfba3b9a448b1f5e46fa inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top"><a class="el" href="classEigen_1_1SVDBase.html">SVDBase</a>&lt; Derived &gt; &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">derived</a> ()</td></tr>
<tr class="separator:a1fbabe7f12bcbfba3b9a448b1f5e46fa inherit pub_methods_classEigen_1_1SolverBase"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:afd4f3f1c57b7594b96a7e30f2974ea2e inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1SVDBase.html">SVDBase</a>&lt; Derived &gt; &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#afd4f3f1c57b7594b96a7e30f2974ea2e">derived</a> () const</td></tr>
<tr class="separator:afd4f3f1c57b7594b96a7e30f2974ea2e inherit pub_methods_classEigen_1_1SolverBase"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a7fd647d110487799205df6f99547879d inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1Solve.html">Solve</a>&lt; <a class="el" href="classEigen_1_1SVDBase.html">SVDBase</a>&lt; Derived &gt;, Rhs &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#a7fd647d110487799205df6f99547879d">solve</a> (const <a class="el" href="classEigen_1_1MatrixBase.html">MatrixBase</a>&lt; Rhs &gt; &amp;b) const</td></tr>
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<tr class="memitem:a4d5e5baddfba3790ab1a5f247dcc4dc1 inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#a4d5e5baddfba3790ab1a5f247dcc4dc1">SolverBase</a> ()</td></tr>
<tr class="separator:a4d5e5baddfba3790ab1a5f247dcc4dc1 inherit pub_methods_classEigen_1_1SolverBase"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a70cf5cd1b31dbb4f4d61c436c83df6d3 inherit pub_methods_classEigen_1_1SolverBase"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classEigen_1_1Transpose.html">ConstTransposeReturnType</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classEigen_1_1SolverBase.html#a70cf5cd1b31dbb4f4d61c436c83df6d3">transpose</a> () const</td></tr>
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<tr class="inherit_header pub_methods_structEigen_1_1EigenBase"><td colspan="2" onclick="javascript:toggleInherit('pub_methods_structEigen_1_1EigenBase')"><img src="closed.png" alt="-"/>&#160;Public Member Functions inherited from <a class="el" href="structEigen_1_1EigenBase.html">Eigen::EigenBase&lt; Derived &gt;</a></td></tr>
<tr class="memitem:a2d768a9877f5f69f49432d447b552bfe inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">EIGEN_CONSTEXPR <a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#a2d768a9877f5f69f49432d447b552bfe">cols</a> () const EIGEN_NOEXCEPT</td></tr>
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<tr class="memitem:a1fbabe7f12bcbfba3b9a448b1f5e46fa inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">Derived &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">derived</a> ()</td></tr>
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<tr class="memitem:afd4f3f1c57b7594b96a7e30f2974ea2e inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">const Derived &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#afd4f3f1c57b7594b96a7e30f2974ea2e">derived</a> () const</td></tr>
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<tr class="memitem:ac22eb0695d00edd7d4a3b2d0a98b81c2 inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">EIGEN_CONSTEXPR <a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">rows</a> () const EIGEN_NOEXCEPT</td></tr>
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<tr class="memitem:ae106171b6fefd3f7af108a8283de36c9 inherit pub_methods_structEigen_1_1EigenBase"><td class="memItemLeft" align="right" valign="top">EIGEN_CONSTEXPR <a class="el" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="structEigen_1_1EigenBase.html#ae106171b6fefd3f7af108a8283de36c9">size</a> () const EIGEN_NOEXCEPT</td></tr>
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<tr class="memdesc:abed06fc6f4b743e1f76a7b317539da87"><td class="mdescLeft">&#160;</td><td class="mdescRight">Default Constructor.  <a href="classEigen_1_1SVDBase.html#abed06fc6f4b743e1f76a7b317539da87">More...</a><br /></td></tr>
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<dl class="deprecated"><dt><b><a class="el" href="deprecated.html#_deprecated000039">Deprecated:</a></b></dt><dd>since <a class="el" href="namespaceEigen.html" title="Namespace containing all symbols from the Eigen library.">Eigen</a> 3.3 </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#abed06fc6f4b743e1f76a7b317539da87">&#9670;&nbsp;</a></span>SVDBase()</h2>

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<p>Default Constructor. </p>
<p>Default constructor of <a class="el" href="classEigen_1_1SVDBase.html" title="Base class of SVD algorithms.">SVDBase</a> </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a705a7c2709e1624ccc19aa748a78d473">&#9670;&nbsp;</a></span>computeU()</h2>

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<dl class="section return"><dt>Returns</dt><dd>true if <em>U</em> (full or thin) is asked for in this SVD decomposition </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a5f12efcb791eb007d4a4890ac5255ac4">&#9670;&nbsp;</a></span>computeV()</h2>

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<dl class="section return"><dt>Returns</dt><dd>true if <em>V</em> (full or thin) is asked for in this SVD decomposition </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a06c311bc452dc1ca5abce2f640e15292">&#9670;&nbsp;</a></span>info()</h2>

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<p>Reports whether previous computation was successful. </p>
<dl class="section return"><dt>Returns</dt><dd><code>Success</code> if computation was successful. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#afc7fe1546b0f6e1801b86f22f5664cb8">&#9670;&nbsp;</a></span>matrixU()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the <em>U</em> matrix.</dd></dl>
<p>For the SVD decomposition of a n-by-p matrix, letting <em>m</em> be the minimum of <em>n</em> and <em>p</em>, the U matrix is n-by-n if you asked for <a class="el" href="group__enums.html#ggae3e239fb70022eb8747994cf5d68b4a9a9fa9302d510cee20c26311154937e23f">ComputeFullU </a>, and is n-by-m if you asked for <a class="el" href="group__enums.html#ggae3e239fb70022eb8747994cf5d68b4a9aa7fb4e98834788d0b1b0f2b8467d2527">ComputeThinU </a>.</p>
<p>The <em>m</em> first columns of <em>U</em> are the left singular vectors of the matrix being decomposed.</p>
<p>This method asserts that you asked for <em>U</em> to be computed. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a245a453b5e7347f737295c23133238c4">&#9670;&nbsp;</a></span>matrixV()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the <em>V</em> matrix.</dd></dl>
<p>For the SVD decomposition of a n-by-p matrix, letting <em>m</em> be the minimum of <em>n</em> and <em>p</em>, the V matrix is p-by-p if you asked for <a class="el" href="group__enums.html#ggae3e239fb70022eb8747994cf5d68b4a9a36581f7c662f7def31efd500c284f930">ComputeFullV </a>, and is p-by-m if you asked for <a class="el" href="group__enums.html#ggae3e239fb70022eb8747994cf5d68b4a9a540036417bfecf2e791a70948c227f47">ComputeThinV </a>.</p>
<p>The <em>m</em> first columns of <em>V</em> are the right singular vectors of the matrix being decomposed.</p>
<p>This method asserts that you asked for <em>V</em> to be computed. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#afe8a555f38393a319a71ec0f0331c9ef">&#9670;&nbsp;</a></span>nonzeroSingularValues()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the number of singular values that are not exactly 0 </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a30b89e24f42f1692079eea31b361d26a">&#9670;&nbsp;</a></span>rank()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the rank of the matrix of which <code>*this</code> is the SVD.</dd></dl>
<dl class="section note"><dt>Note</dt><dd>This method has to determine which singular values should be considered nonzero. For that, it uses the threshold value that you can control by calling <a class="el" href="classEigen_1_1SVDBase.html#a1c95d05398fc15e410a28560ef70a5a6">setThreshold(const RealScalar&amp;)</a>. </dd></dl>

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<h2 class="memtitle"><span class="permalink"><a href="#a1c95d05398fc15e410a28560ef70a5a6">&#9670;&nbsp;</a></span>setThreshold() <span class="overload">[1/2]</span></h2>

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<p>Allows to prescribe a threshold to be used by certain methods, such as <a class="el" href="classEigen_1_1SVDBase.html#a30b89e24f42f1692079eea31b361d26a">rank()</a> and <a class="el" href="classEigen_1_1SVDBase.html#ab28499936c0764fe5b56b9f4de701e26">solve()</a>, which need to determine when singular values are to be considered nonzero. This is not used for the SVD decomposition itself.</p>
<p>When it needs to get the threshold value, <a class="el" href="namespaceEigen.html" title="Namespace containing all symbols from the Eigen library.">Eigen</a> calls <a class="el" href="classEigen_1_1SVDBase.html#a98b2ee98690358951807353812a05c69">threshold()</a>. The default is <code>NumTraits&lt;Scalar&gt;::epsilon()</code> </p>
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<p>A singular value will be considered nonzero if its value is strictly greater than \( \vert singular value \vert \leqslant threshold \times \vert max singular value \vert \).</p>
<p>If you want to come back to the default behavior, call <a class="el" href="classEigen_1_1SVDBase.html#a27586b69dbfb63f714d1d45fd6304f97">setThreshold(Default_t)</a> </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a27586b69dbfb63f714d1d45fd6304f97">&#9670;&nbsp;</a></span>setThreshold() <span class="overload">[2/2]</span></h2>

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<p>Allows to come back to the default behavior, letting <a class="el" href="namespaceEigen.html" title="Namespace containing all symbols from the Eigen library.">Eigen</a> use its default formula for determining the threshold.</p>
<p>You should pass the special object Eigen::Default as parameter here. </p><div class="fragment"><div class="line">svd.setThreshold(Eigen::Default); </div>
</div><!-- fragment --><p>See the documentation of <a class="el" href="classEigen_1_1SVDBase.html#a1c95d05398fc15e410a28560ef70a5a6">setThreshold(const RealScalar&amp;)</a>. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#a4e7bac123570c348f7ed6be909e1e474">&#9670;&nbsp;</a></span>singularValues()</h2>

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<dl class="section return"><dt>Returns</dt><dd>the vector of singular values.</dd></dl>
<p>For the SVD decomposition of a n-by-p matrix, letting <em>m</em> be the minimum of <em>n</em> and <em>p</em>, the returned vector has size <em>m</em>. Singular values are always sorted in decreasing order. </p>

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<h2 class="memtitle"><span class="permalink"><a href="#ab28499936c0764fe5b56b9f4de701e26">&#9670;&nbsp;</a></span>solve()</h2>

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          <td class="memname">const <a class="el" href="classEigen_1_1Solve.html">Solve</a>&lt;Derived, Rhs&gt; <a class="el" href="classEigen_1_1SVDBase.html">Eigen::SVDBase</a>&lt; Derived &gt;::solve </td>
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<dl class="section return"><dt>Returns</dt><dd>a (least squares) solution of \( A x = b \) using the current SVD decomposition of A.</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
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    <tr><td class="paramname">b</td><td>the right-hand-side of the equation to solve.</td></tr>
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<dl class="section note"><dt>Note</dt><dd>Solving requires both U and V to be computed. Thin U and V are enough, there is no need for full U or V.</dd>
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SVD solving is implicitly least-squares. Thus, this method serves both purposes of exact solving and least-squares solving. In other words, the returned solution is guaranteed to minimize the Euclidean norm \( \Vert A x - b \Vert \). </dd></dl>

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<a id="a98b2ee98690358951807353812a05c69"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a98b2ee98690358951807353812a05c69">&#9670;&nbsp;</a></span>threshold()</h2>

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template&lt;typename Derived &gt; </div>
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          <td class="memname">RealScalar <a class="el" href="classEigen_1_1SVDBase.html">Eigen::SVDBase</a>&lt; Derived &gt;::threshold </td>
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<p>Returns the threshold that will be used by certain methods such as <a class="el" href="classEigen_1_1SVDBase.html#a30b89e24f42f1692079eea31b361d26a">rank()</a>.</p>
<p>See the documentation of <a class="el" href="classEigen_1_1SVDBase.html#a1c95d05398fc15e410a28560ef70a5a6">setThreshold(const RealScalar&amp;)</a>. </p>

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<hr/>The documentation for this class was generated from the following file:<ul>
<li><a class="el" href="SVDBase_8h_source.html">SVDBase.h</a></li>
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